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Block #1,630,868

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/16/2016, 8:20:07 AM Β· Difficulty 10.6069 Β· 5,195,855 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
9a1daa71b2d558397d28de94aabcb0b74065a5c40c7b875d675e787d60e07fa7
View on Chainz β†—

Height

#1,630,868

Difficulty

10.606866

Transactions

2

Size

425 B

Version

2

Bits

0a9b5b8d

Nonce

1,225,739,289

Timestamp

6/16/2016, 8:20:07 AM

Confirmations

5,195,855

Mined by

⛏️ P2SHAcFQFk56rchVnkh4yZr4f4xBGKCCsZE5jk

Merkle Root

8ace0512f0767f7bf2b1e10908e0431f511442f6728b4a949f0a4a8139f3cec3
Transactions (2)
Coinbaseb3c842fdb5e356…bf279e5b8ebbcb
1 in β†’ 1 out8.8800 XPM109 B
AcFQFk56…CCsZE5jk
9e5c5be383619b…9557127492448b
1 in β†’ 2 out548.4622 XPM226 B
AR1eaXi7…iVTtCTVyAe5fUy13…BrrWut7K
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

6.298 Γ— 10⁹⁴(95-digit number)
62988475604749304945…94214431076637900159
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
6.298 Γ— 10⁹⁴(95-digit number)
62988475604749304945…94214431076637900159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.298 Γ— 10⁹⁴(95-digit number)
62988475604749304945…94214431076637900161
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
1.259 Γ— 10⁹⁡(96-digit number)
12597695120949860989…88428862153275800319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.259 Γ— 10⁹⁡(96-digit number)
12597695120949860989…88428862153275800321
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
2.519 Γ— 10⁹⁡(96-digit number)
25195390241899721978…76857724306551600639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.519 Γ— 10⁹⁡(96-digit number)
25195390241899721978…76857724306551600641
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
5.039 Γ— 10⁹⁡(96-digit number)
50390780483799443956…53715448613103201279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.039 Γ— 10⁹⁡(96-digit number)
50390780483799443956…53715448613103201281
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
1.007 Γ— 10⁹⁢(97-digit number)
10078156096759888791…07430897226206402559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.007 Γ— 10⁹⁢(97-digit number)
10078156096759888791…07430897226206402561
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜†β˜†β˜†
Rarity
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,857,938 XPMΒ·at block #6,826,722 Β· updates every 60s
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